Rough paths

 

This page is dedicated to gather informations on rough paths theory.

bib file of the bibliography below.

 

People

  • Peter K. Friz (Cambridge) [www]
  • Massimiliano Gubinelli (Orsay) [www]

 

Preprints

  1. M. Gubinelli. Ramification of rough paths. 2006. (arXiv)
  2. M. Gubinelli. Rough solutions of the periodic Korteweg-de Vries equation. 2006. (arXiv)
  3. P. Friz and N. Victoir. The burkholder-davis-gundy inequality for enhanced martingales. 2006. (arXiv)
  4. P. Friz and N. Victoir. Euler estimates for rough differential equations. 2006.
  5. P. Friz and N. Victoir. A note on the notion of geometric rough paths. 2004.
  6. P. Friz and N. Victoir. On uniformly subelliptic operators and stochastic area. 2006. (arXiv)
  7. D. Feyel and A. de La Pradelle. Curvilinear integrals along enriched paths. 2005.

 

Books

  1. T. Lyons and Z. Qian. System Control and Rough PathsOxford University Press, 2002.

 

Papers

  1. L. Coutin and Z. Qian. Stochastic differential equations for fractional Brownian motions. C. R. Acad. Sci. Paris Sér. I Math.331(1):75–80, 2000.
  2. L. Coutin and Z. Qian. Stochastic analysis, rough path analysis and fractional Brownian motions. Probab. Theory Related Fields122(1):108–140, 2002.
  3. A. M. Davie. Differential equations driven by rough signals: an approach via discrete approximation. 2003.
  4. H. Bessaih, M. Gubinelli, and F. Russo. The evolution of a random vortex filament. Ann. Probab.33(5):1825–1855, 2005. (arXiv)
  5. J. G. Gaines and T. Lyons. Random generation of stochastic area integrals. SIAM J. Appl. Math.54(4):1132–1146, 1994.
  6. J. G. Gaines and T. Lyons. Variable step size control in the numerical solution of stochastic differential equations. SIAM J. Appl. Math.57(5):1455–1484, 1997.
  7. B. Hambly and T. Lyons. Uniqueness for the Signature of a Path of Bounded Variation. 2002.
  8. B. Hambly and T. Lyons. Stochastic area for Brownian motion on the Sierpinski gasket. Ann. Probab.26(1):132–148, 1998.
  9. M. Ledoux, T. Lyons, and Z. Qian. Lévy area of Wiener processes in Banach spaces. Ann. Probab.30(2):546–578, 2002.
  10. M. Ledoux, Z. Qian, and T. Zhang. Large deviations and support theorem for diffusion processes via rough paths. 2002.
  11. A. Lejay. Stochastic differential equations driven by a processes generated by divergence form operators. 2002.
  12. A. Lejay. An introduction to rough paths. 2002.
  13. X. D. Li and T. Lyons. Smoothness of the Itô map on p-rough path spaces (I): 1 < p < 2. 2002.
  14. T. Lyons. Differential equations driven by rough signals. I. An extension of an inequality of L. C. Young. Math. Res. Lett.1(4):451–464, 1994.
  15. T. Lyons. The interpretation and solution of ordinary differential equations driven by rough signals. In Stochastic analysis (Ithaca, NY, 1993)pages 115–128. Amer. Math. Soc., Providence, RI, 1995.
  16. T. Lyons. Differential equations driven by rough signals. Rev. Mat. Iberoamericana14(2):215–310, 1998.
  17. T. Lyons and A. Lejay. On the importance of the Lévy area for systems controlled by converging stochastic processes. application to homogenization. 2002.
  18. T. Lyons and Z. Qian. System Control and Rough PathsOxford University Press, 2002.
  19. T. Lyons and Z. Qian. Calculus for multiplicative functionals, Itô’s formula and differential equations. In Itô’s stochastic calculus and probability theorypages 233–250. Springer, Tokyo, 1996.
  20. T. Lyons and Z. Qian. A class of vector fields on path spaces. J. Funct. Anal.145(1):205–223, 1997.
  21. T. Lyons and Z. Qian. Stochastic Jacobi fields and vector fields induced by varying area on path spaces. Probab. Theory Related Fields109(4):539–570, 1997.
  22. T. Lyons and Z. Qian. Flow equations on spaces of rough paths. J. Funct. Anal.149(1):135–159, 1997.
  23. T. Lyons and Z. Qian. Calculus of variation for multiplicative functionals. In New trends in stochastic analysis (Charingworth, 1994)pages 348–374. World Sci. Publishing, River Edge, NJ, 1997.
  24. T. Lyons and Z. Qian. Flow of diffeomorphisms induced by a geometric multiplicative functional. Probab. Theory Related Fields112(1):91–119, 1998.
  25. T. Lyons and L. Stoica. On the limit of stochastic integrals of differential forms. In Stochastic processes and related topics (Siegmundsberg, 1994)pages 61–66. Gordon and Breach, Yverdon, 1996.
  26. T. Lyons and L. Stoica. The limits of stochastic integrals of differential forms. Ann. Probab.27(1):1–49, 1999.
  27. T. Lyons and N. Victoir. Cubature on Wiener space. 2002.
  28. T. Lyons and O. Zeitouni. Conditional exponential moments for iterated Wiener integrals. Ann. Probab.27(4):1738–1749, 1999.
  29. A. Lejay. An introduction to rough paths. In Séminaire de Probabilités XXXVIIvolume 1832 of Lecture Notes in Math.pages 1–59. Springer, Berlin, 2003.
  30. M. Gubinelli. Controlling rough paths. J. Funct. Anal.216(1):86–140, 2004.
  31. P. Friz and N. Victoir. Approximations of the Brownian rough path with applications to stochastic analysis. Ann. Inst. H. Poincaré Probab. Statist.41(4):703–724, 2005.
  32. L. Coutin and A. Lejay. Semi-martingales and rough paths theory. Electron. J. Probab.10:no. 23, 761–785 (electronic), 2005.
  33. E.-M. Sipiläinen. A pathwise view of solutions of stochastic differential equations. PhD thesis, University of Edinburgh, 1993.
  34. D. R. E. Williams. Diffeomorphic flows driven by Lévy processes. 2000.
  35. D. R. E. Williams. Path-wise solutions of stochastic differential equations driven by Lévy processes. Rev. Mat. Iberoamericana17(2):295–329, 2001.
  36. D. R. E. Williams. Solutions of differential equations driven by càdlàg paths of finite p-variation. PhD thesis, Imperial College, London, 1998.
  37. A. Lejay, M. Gubinelli, and S. Tindel. Young integrals and SPDEs. Pot. Anal.2006. to appear. (arXiv)

 

Related works

  1. R. Azencott. Formule de Taylor stochastique et développement asymptotique d’intégrales de Feynman. In Seminar on Probability, XVI, Supplementpages 237–285. Springer, Berlin, 1982.
  2. R. F. Bass, B. Hambly, and T. Lyons. Extending the Wong-Zakai theorem to reversible Markov processes. 2001.
  3. G. Ben Arous. Flots et séries de Taylor stochastiques. Probab. Theory Related Fields81(1):29–77, 1989.
  4. N. Bouleau and D. Lépingle. Numerical methods for stochastic processesJohn Wiley & Sons Inc., New York, 1994.
  5. N. Bourbaki. Éléments de mathématique. Fasc. XXXVII. Groupes et algèbres de Lie. Chapitre II: Algèbres de Lie libres. Chapitre III: Groupes de LieHermann, Paris, 1972.
  6. K. Burrage and P. M. Burrage. Order conditions of stochastic Runge-Kutta methods by B-series. SIAM J. Numer. Anal.38(5):1626–1646 (electronic), 2000.
  7. M. Capitaine and C. Donati-Martin. The Lévy area process for the free Brownian motion. J. Funct. Anal.179(1):153–169, 2001.
  8. F. Castell. Asymptotic expansion of stochastic flows. Probab. Theory Related Fields96(2):225–239, 1993.
  9. F. Castell and J. Gaines. An efficient approximation method for stochastic differential equations by means of the exponential Lie series. Math. Comput. Simulation38(1-3):13–19, 1995.
  10. F. Castell and J. Gaines. The ordinary differential equation approach to asymptotically efficient schemes for solution of stochastic differential equations. Ann. Inst. H. Poincaré Probab. Statist.32(2):231–250,1996.
  11. K.-T. Chen. Integration of paths, geometric invariants and a generalized Baker-Hausdorff formula. Ann. of Math. (2)65:163–178, 1957.
  12. K.-T. Chen. Integration of paths—a faithful representation of paths by non-commutative formal power series. Trans. Amer. Math. Soc.89:395–407, 1958.
  13. V. V. Chistyakov and O. E. Galkin. On maps of bounded p-variation with p > 1. Positivity2(1):19–45, 1998.
  14. H. Doss. Liens entre équations différentielles stochastiques et ordinaires. C. R. Acad. Sci. Paris Sér. A-B283(13):Ai, A939–A942, 1976.
  15. H. Doss. Liens entre équations différentielles stochastiques et ordinaires. Ann. Inst. H. Poincaré Sect. B (N.S.)13(2):99–125, 1977.
  16. R. Dudley and R. Norvaiša. An introduction to p-variation and Young integrals – with emphasis on sample functions of stochastic processes. 1998.
  17. R. M. Dudley and R. Norvaiša. Differentiability of six operators on nonsmooth functions and p-variationvolume 1703 of Lecture Notes in MathematicsSpringer-Verlag, Berlin, 1999.
  18. H. Föllmer. Calcul d’Itô sans probabilités. In Seminar on Probability, XV (Univ. Strasbourg, Strasbourg, 1979/1980) (French)pages 143–150. Springer, Berlin, 1981.
  19. Y. Z. Hu. Série de Taylor stochastique et formule de Campbell-Hausdorff, d’après Ben Arous. In Séminaire de Probabilités, XXVIvolume 1526 of Lecture Notes in Math.pages 579–586. Springer, Berlin, 1992.
  20. N. Ikeda and S. Watanabe. Stochastic differential equations and diffusion processesNorth-Holland Publishing Co., Amsterdam, 1981.
  21. N. Ikeda and S. Watanabe. Stochastic differential equations and diffusion processesNorth-Holland Publishing Co., Amsterdam, second edition, 1989.
  22. P. Kloeden and E. Platen. Numerical solution of stochastic differential equationsSpringer-Verlag, Berlin, 1992.
  23. P. Kloeden, E. Platen, and H. Schurz. Numerical solution of SDE through computer experimentsSpringer-Verlag, Berlin, 1994.
  24. H. Kunita. On the representation of solutions of stochastic differential equations. In Seminar on Probability, XIV (Paris, 1978/1979) (French)pages 282–304. Springer, Berlin, 1980.
  25. P. Lévy. Wiener’s random function, and other Laplacian random functions. In Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 1950, pages 171–187, Berkeley and Los Angeles, 1951. University of California Press.
  26. P. Lévy. Processus stochastiques et mouvement brownienGauthier-Villars & Cie, Paris, 1965.
  27. P. Lévy. Processus stochastiques et mouvement brownienÉditions Jacques Gabay, Sceaux, 1992.
  28. S. Lototsky. Small perturbation of stochastic parabolic equations: a power series analysis. J. Funct. Anal.193(1):94–115, 2002.
  29. P.-A. Meyer. Sur deux estimations d’intégrales multiples. In Séminaire de Probabilités, XXVvolume 1485 of Lecture Notes in Math.pages 425–426. Springer, Berlin, 1991.
  30. J. C. Butcher. An algebraic theory of integration methods. Math. Comp.26:79–106, 1972.
  31. K. T. Chen. Iterated path integrals. Bull. Amer. Math. Soc.83(5):831–879, 1977.
  32. K.-T. Chen. Collected papers of K.-T. ChenContemporary Mathematicians. Birkhäuser Boston Inc., Boston, MA, 2001.
  33. E. Platen. A Taylor formula for semimartingales solving a stochastic equation. In Stochastic differential systems (Visegrád, 1980)pages 157–164. Springer, Berlin, 1981.
  34. E. Platen and W. Wagner. On a Taylor formula for a class of Itô processes. Probab. Math. Statist.3(1):37–51 (1983), 1982.
  35. C. Reutenauer. Free Lie algebrasThe Clarendon Press Oxford University Press, New York, 1993.
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  38. V. S. Varadarajan. Lie groups, Lie algebras, and their representationsvolume 102 of Graduate Texts in MathematicsSpringer-Verlag, New York, 1984.
  39. Y. Yamato. Stochastic differential equations and nilpotent Lie algebras. Z. Wahrsch. Verw. Gebiete47(2):213–229, 1979.
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